GCSE Maths Practice: two-way-tables

Survey questions based on preferences are very common in probability. In these situations, people are often allowed to choose more than one option. This means that the groups described in the question can overlap, and this overlap must be handled carefully.

The aim of this question is to find the chance that a randomly selected student prefers at least one of the drinks. This includes students who prefer only one drink as well as students who prefer both drinks.

One helpful way to understand this is to imagine asking students to stand in lines. One line represents students who prefer the first drink, and another line represents students who prefer the second drink. Some students may stand in both lines because they like both drinks. Even though they appear twice, they are still just one student.

To count correctly, imagine calling students forward one at a time. You count each student only once, no matter how many preferences they have. This helps avoid the common mistake of double counting.

Here is a similar example. Suppose a group of people are asked whether they like pizza or pasta. Some people like both. If you want to know the probability that a randomly chosen person likes pizza or pasta, you must count everyone who likes at least one of them, but you must not count people who like both twice.

Once you have the correct number of students who meet the condition, finding the probability is straightforward. Probability is the number of favourable outcomes divided by the total number of possible outcomes. In survey questions, the total number of outcomes is the total number of people surveyed.

These questions are popular at GCSE Foundation level because they test understanding and organisation rather than difficult calculations. Many mistakes happen when students rush and forget to think about overlap.

In real life, this type of reasoning is used when planning events, choosing products, or analysing survey results. Correct counting helps ensure fair decisions and accurate conclusions.

A good exam habit is to stop before answering and ask yourself whether any student could belong to both groups. If so, make sure your method counts each student only once before calculating the probability.